Queuing Models and Analyses of Traffic Control

Abstract

This dissertation investigates queuing modeling and related analyses of traffic control at signalized intersections and ramp meters. A primary goal in this dissertation is to apply queuing theory to vehicular traffic control systems, including adaptive traffic signal control, fixed-time traffic signal control, actuated traffic signal control and ramp metering control.First, a simple two-phase traffic adaptive control scheme is studied, where the traffic signal serves one queue until it dissipates and then serves the accumulated queue in the other direction. Distribution of cycle length and average delay at steady-state is obtained by an iterative algorithm.Second, a two-phase fixed-time signal control for an isolated intersection with Poisson arrivals is modeled and analyzed. Distribution of residual queue length and average delay is calculated cycle by cycle until the steady state is reached.Third, an eight-phase actuated signal control is analyzed. Distribution of actuated phase length, corresponding residual queue and delay at steady-state is obtained by iterative algorithm. The other direction, whose phase length is determined by the actuated phase, is then analyzed analytically.The last model analyzes a ramp metering system. By developing a state transition matrix and corresponding steady-state equations, the steady-state queue length distribution can be calculated analytically. Comparing the model results with an occupancy measure of an upstream ramp detector allows one to estimate the arrival rate at the ramp meter.In all of the queuing models developed for the above applications, iterative algorithms are developed to calculate steady probabilities for various measures. The results from the algorithms are compared with those obtained from simulations. In all cases they matched well.